The Bees made a dream start when full-back Mark Byrne saw his 25-yard free kick take a big deflection past goalkeeper Ross Atkins after only six minutes.
But Burton were back on level terms in the 27th minute when midfielder Jacques Maghoma fired home from the edge of the box.
Calvin Zola could have added to the worries of the travelling fans in the 43rd minute but shot wildly over the crossbar from the penalty spot. And the pendulum swung back in the favour of Londoners when Mark Hughes squeezed home his left-footed volley from the edge of the area.
Allen said: "It was a nervy afternoon and we didn't play well first half, but I suppose that was to be expected because of the tension, anxiety and the build-up of the whole week. But I thought, second half, the players stepped up to the mark and we played really, really well.
"All the credit has got to the players for the way they responded when we needed them to. It was always going to be a nervous occasion because 10 months of work all came down to the final afternoon of the season.
"The credit has got to the players because to win back-to-back games at this stage of the season is a fantastic effort."
